Uncertainty Distribution Arithmetic With Correlation Tracking
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Solution Overview
Problem
Existing computer architectures lack support for representing and performing arithmetic operations on uncertainty distributions, leading to insufficient accuracy and inefficiency in handling uncertain data.
Innovation Solution
A computer-implemented method and system for computation on distributions, utilizing Joint Telescoping Torques Distribution Representation (jTTR) to represent and perform arithmetic operations on distributional variables, including correlation tracking to maintain accuracy and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If single particle values are used to represent uncertain data, then computation simplicity is improved, but measurement precision deteriorates
Solution Approach 1:
The patent segments uncertain data representation into discrete particles, where each particle carries a specific value and probability weight. This segmentation allows the system to maintain computational simplicity by working with discrete elements while improving measurement precision by preserving the distribution characteristics of uncertain data through multiple particles rather than collapsing to a single mean value.
Solution Approach 2:
The patent changes the parameter representation from single mean values to distributions of particles with associated probabilities. This parameter transformation enables the system to represent uncertainty more accurately by maintaining the full distribution information while still allowing efficient computation through particle-based arithmetic operations.
2Measurement precision
If correlation information is tracked in arithmetic operations, then measurement precision is improved, but device complexity worsens
Solution Approach 1:
The patent implements feedback by tracking correlation information between particles throughout arithmetic operations. The system monitors how particles from different input distributions interact and maintains correlation metadata that feeds back into subsequent calculations. This feedback mechanism improves measurement precision by accounting for dependencies while managing complexity through structured correlation tracking rather than full probabilistic modeling.
Solution Approach 2:
The patent introduces correlation information as an intermediary element that mediates between simple particle values and complex probabilistic dependencies. This intermediary allows the system to capture essential correlation effects without requiring full joint distribution representations, thereby improving accuracy while limiting complexity growth.
3Measurement precision
If distribution representations are used instead of single values, then measurement precision is improved, but productivity worsens
Solution Approach 1:
The patent segments continuous distributions into discrete particle representations, transforming complex distribution manipulations into simpler particle-based operations. This segmentation improves measurement precision by preserving distribution characteristics while enhancing productivity by enabling efficient particle arithmetic that scales better than full distribution computations.
Solution Approach 2:
The patent uses particle copies to represent distribution samples, where each particle is a simplified copy carrying essential distribution information. This copying approach improves productivity by working with lightweight particle objects rather than complex distribution functions, while maintaining measurement precision through sufficient particle sampling that captures the underlying distribution behavior.
Data Source
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AI summary
The present disclosure relates to a computer-implemented method for computation on distributions, comprising: obtaining at least a first representation of a first distributional variable and a second representation of a second distributional variable; and executing an arithmetic operation on the first representation and the second representation to obtain a computation result in the form of a third representation of a third distributional variable, wherein executing the arithmetic operation on the first representation and the second representation is based on, or includes, correlation information, which indicates a correlation of at least one of the first representation and the second representation with one or more correlated distributional variables.